Mach 10 Shock Wave — ANSYS Fluent

 Simulating a Mach 10 shock wave in Ansys Fluent involves the hypersonic flow regime, where extreme temperatures and thermochemical effects dominate the physics.

1. Introduction and Physical Meaning

Hypersonic flow, generally defined as flow above Mach 5, is characterized by very strong shock waves and massive temperature increases behind the shock. At Mach 10, the gas can no longer be treated as inert; kinetic energy is converted into internal energy to a degree that activates vibrational and electronic excitation.

As enthalpies rise, chemical reactions such as dissociation and ionization begin (e.g., oxygen dissociation starts at 2000 K). A critical challenge is thermo-chemical non-equilibrium, occurring when the flow timescale is similar to the time needed for internal energy modes to relax or for chemical reactions to complete. This may also involve physical phenomena like radiation and wall catalysis.

2. Procedure in Ansys Fluent

Modeling these high-energy flows requires the Density-Based Solver (DBNS) due to the strong coupling between the continuity, momentum, and energy equations.

• Solver Setup: In the General task page, select the Density-Based solver with an Implicit formulation. Ensure Double Precision is enabled to manage high pressure gradients and energy balances.
• High-Speed Numerics (HSN): Enable HSN in the Solution Methods task page. While the Adaptive mode (Regime 5) is the default, for Mach 10, you can manually select the Hypersonic (Regime 4) setting for increased stabilization.
• Physical Models:
  • Enable the Energy Equation.
  • For thermal non-equilibrium, select the Two-Temperature Model.
  • Activate Species Transport with Finite Rate Chemistry (selecting the None - Direct Source solver for DBNS).
• Mixture Selection: Use air-5species if temperatures are moderate, or air-11species (using Park or Gupta mechanisms) for weakly ionized flows above 10,000 K.
• Initialization: Use Full Multigrid (FMG) Initialization to provide a robust starting field and prevent solver divergence.

3. Numerical Parameters and Best Practices

To ensure accuracy and stability in hypersonic simulations, follow these technical guidelines:

• Solution Limits: The default maximum temperature limit of 5000 K is often too low for Mach 10. It must be increased in Solution → Controls → Limits to avoid unphysical clipping and residual stagnation.
• Gradient Evaluation: If the mesh is unstructured or skewed, use the Green-Gauss Node-Based method for better accuracy near discontinuities.
• Mesh Resolution (\(y^+\)): To accurately resolve the boundary layer in viscous hypersonic flows, a wall-normal resolution of \(y^+ \approx 1\) is recommended.
• Shock Visualization: Use the Pressure Discontinuity Sensor field variable (in the Pressure category) to identify and visualize the strongest parts of the shock front.
• CFL Control: If convergence is difficult, stabilize the solution by starting with a conservative Courant (CFL) value.

4. Summary for the Practitioner

Checklist for Mach 10 Simulations:

• [ ] Solver: Density-Based Implicit formulation.
• [ ] HSN: High-Speed Numerics enabled (Regime 4 or 5).
• [ ] Physics: Energy equation, Two-Temperature model, and Species Transport.
• [ ] Limits: Maximum temperature limit increased above 5000 K.
• [ ] Initialization: FMG initialization executed.
• [ ] Validation: Verify the Net Imbalance in Flux Reports is less than 1%.
• [ ] Post-processing: Monitor shock wave stability and check for oscillations in total heat-flux contours.